Nonhuman primate models are needed for evaluations of proposed strategies targeting residual virus that persists in HIV-1-infected individuals receiving suppressive combination antiretroviral therapy (cART). However, relevant nonhuman primate (NHP) models of cART-mediated suppression have proven challenging to develop. We used a novel three-class, six-drug cART regimen to achieve durable 4.0- to 5.5-log reductions in plasma viremia levels and declines in cell-associated viral RNA and DNA in blood and tissues of simian immunodeficiency virus SIVmac239-infected Indian-origin rhesus macaques, then evaluated the impact of treatment with the histone deacetylase inhibitor (HDACi) suberoylanilide hydroxamic acid (SAHA; Vorinostat) on the residual virus pool. Ex vivo SAHA treatment of CD4⁺ T cells obtained from cART-suppressed animals increased histone acetylation and viral RNA levels in culture supernatants. cART-suppressed animals each received 84 total doses of oral SAHA. We observed SAHA dose-dependent increases in acetylated histones with evidence for sustained modulation as well as refractoriness following prolonged administration. In vivo virologic activity was demonstrated based on the ratio of viral RNA to viral DNA in peripheral blood mononuclear cells, a presumptive measure of viral transcription, which significantly increased in SAHA-treated animals. However, residual virus was readily detected at the end of treatment, suggesting that SAHA alone may be insufficient for viral eradication in the setting of suppressive cART. The effects observed were similar to emerging data for repeat-dose SAHA treatment of HIV-infected individuals on cART, demonstrating the feasibility, utility, and relevance of NHP models of cART-mediated suppression for in vivo assessments of AIDS virus functional cure/eradication approaches.